I know this sounds crazy, but is it possible to run a non-Steam SRCDS for a game I have on my Steam account?

I downloaded SRCDS on this site and followed the guide and set it up accordingly and then downloaded a gungame mod, maps and all its dependencies, but I can't get it to work. The server doesn't show up in my server list and won't even be added to my favorites list if I manually enter the IP and port.

I don't have any IP address in the startup command. I take it this isn't possible to have a SRCDS which doesn't rely on Steam, to run on Source which I have on Steam? I technically didn't buy Source through Steam, I merely used a serial key from my disc-copy.

I run Windows 7 x64, if it matters.

I guess I could run the Steam-based Dedicated Server, but that requires another Steam account and I don't wish to have two. One is enough.